In geometry, a square is a regular quadrilateral, which means it has four equal sides and four equal angles (90 degrees or (100 degrees or right angles). It can also be defined as a rectangle, in which the length of two adjacent sides is equal. A square with a vertex ABCD is called a square ABCD.

Square is the special case of diamond (equal sides, opposite equal angles), kite (two adjacent equal sides), trapezoid (one opposite side is parallel), parallelogram (all opposite sides are parallel), quadrilateral or quadrilateral (quadrilateral polygon) and rectangle (both sides are equal, right angles), so it has all the attributes of all these shapes

Each acute triangle has three inscribed squares (the inner square, so that all four vertices of the square are on one side of the triangle, so that two of them are on the same side, so that one side of the square coincides with one part of the side). In a right triangle, two squares coincide and have a vertex at the right angle of the triangle, so a right triangle has only two different inscribed squares. An obtuse triangle has only one inscribed square, and its edge coincides with a part of the longest edge of the triangle.

The proportion of triangle area filled by square shall not exceed 1 / 2.

In non Euclidean geometry, a square is usually a polygon with four equal sides and angles.

In spherical geometry, a square is a polygon, and its edge is a large arc of equal distance, which intersects at equal angles. Unlike a square of plane geometry, the angle of the square is greater than the right angle. A larger spherical square has a larger angle.

In hyperbolic geometry, there is no right square. Instead, the angle of the square in hyperbolic geometry is less than the right angle. The angle of the larger hyperbolic square is smaller.